How about writing a macro for the document that intercepts the document
close event; tests to see if it's been changed; if so, asks the user if the
change should be sent to everyone, and if so, automatically emails a copy of
the document to them?  This won't cause it to automatically be saved by the
recipiants, but at least you've reasonably assured yourself that it's
getting to them every time it changes.

If they're logging into the same network as you are, then you could do
something with login scripts to cause the new copy to be pushed to their
desktops without having to use a sharepoint server (just use xcopy with the
/d and /y switches as part of a login script).

hth,

Chip